Question

The principal value of ${\cos }^{-1}(-\sin \frac{7\pi }{6})$

• A. $\frac{7\pi }{3}$
• B. $\frac{5\pi }{3}$
• C. $\frac{\pi }{3}$
• D. $-\frac{\pi }{3}$

Answer 1

The correct option is C $\frac{\pi }{3}$

${\cos }^{-1}(-\sin \frac{7\pi }{6})={\cos }^{-1}(-\sin (\pi +\frac{\pi }{6}))={\cos }^{-1}\left(\sin \left(\frac{\pi }{6}\right)\right)={\cos }^{-1}\left(\cos \left(\frac{\pi }{3}\right)\right)=\frac{\pi }{3}(\because {\cos }^{-1}(\cos x)=x,x\in [0,\pi \left]\right)$